Is there a term that means "surgically extract"?
Example sentence:
She decided to _ the tumor in her breasts.
The word is excise, and in BrE it's pronounced with the stress on the second syllable to distinguish it from tax (where it's a noun and stressed on the first syllable). The verb excise meaning tax is very rare, and the examples here would never be interpreted as "tax".
excise
verb with object
Cut out surgically.
‘the precision with which surgeons can excise brain tumours’
‘excised tissue’— Oxford
An alternative would be resect. This would avoid any confusion with taxation.
resect
verb
- Cut out (tissue or part of an organ) ‘a small piece of resected colon’
Oxford